No textbook is required — the course is based on these lecture notes, updated as the semester progresses. The books listed under References are optional supplements.
A graduate-level course on the theory and practice of numerical algorithms. The course develops the mathematical foundations of scientific computing: direct methods for linear systems (LU factorization with pivoting), Newton's method for systems of nonlinear equations and its convergence theory, floating-point arithmetic and rounding error analysis, conditioning of problems and stability of algorithms, polynomial and spline interpolation (including B-splines), numerical integration (Newton–Cotes, Gaussian, and adaptive quadrature), and the computation of eigenvalues via unitary similarity transformations and the QR algorithm. Emphasis is placed on rigorous error analysis — in particular the interplay between the conditioning of a problem and the backward stability of an algorithm — alongside efficient implementation.
Prerequisites. Linear algebra and advanced calculus/introductory analysis at the undergraduate level; an undergraduate course in numerical methods (e.g., MATH 4610) is recommended; experience programming in MATLAB, Python, or a similar language.
Topics are tentative and subject to change; updates will be announced in class and on Canvas.
Slides are posted as PDFs after each lecture; a link goes live once the file is uploaded.
Four assignments, 10% each, combining theoretical problems with programming exercises in MATLAB or Python. PDFs are posted here when assigned; solutions appear after the due date.
One in-class midterm exam around the middle of the semester. The exam paper and solutions are posted on USU Box after the exam; both require a USU sign-in to open.
No required textbook. The course follows the lecture notes posted above. Optional references: Numerical Analysis in Modern Scientific Computing: An Introduction, 2nd ed., Deuflhard & Hohmann; Numerical Linear Algebra, Trefethen & Bau; and An Introduction to Numerical Analysis, 2nd ed., Stoer & Bulirsch.
Software. MATLAB is recommended for implementing algorithms and completing assignments.
In lieu of a final exam, each student completes a final project: the implementation and analysis of a numerical method related to the course material, a short written report, and a brief in-class presentation during the last week of classes or the final examination period. Project topics must be approved by the instructor. No exams or quizzes will be given during No-Test Week (December 7–11).
| A | 93–100 | B– | 80–82 | C– | 70–72 |
| A– | 90–92 | C+ | 77–79 | D | 60–69 |
| B+ | 87–89 | C | 73–76 | F | 0–59 |
| B | 83–86 |